The Padé approximation to the the \(k^{2}\)  expansion improves the range of validity of the model greatly by forcing the expansion to smoothly transition to zero as \(k \rightarrow \infty \) .
Not only does this resummation remove high-\(k\)  divergence due to polynomial terms, but it also increases the maximum wavenumber \(k\)  up to which the BB term is a decent approximation to the Fourier transform of an idealized halo profile, which also transitions to zero for large \(k\) . We note that in the EFT sense, the BB term is not “stochastic”, since we do not enforce that it is uncorrelated with the ZA term.
The two-point correlation function (2PCF) is given by the Fourier transform of this expansion, which is analyticTo clarify, we take “analytic” in the sense of closed-form (as in [1]}), rather than in the technical sense of functions., and an expression for which (for \(n_{\rm {max}}=0,1,2\) ) can be found in Appendix .
